Answer:
y=-3x+5
Step-by-step explanation:
As the new line is perpendicular to the original line, the gradient of the new line (m) will be -1 ÷ gradient of original line = -1 ÷ 1/3 =3
the coefficient of x in the expansion of (a x)5 (1-2x)6, where a is positive, is 90. find the value of a.
In the given expansion ,the value of a = -4/3 .
Binomial Distribution:
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments. Each asks a yes-no question and each has its own Boolean outcome: success (probability p) or failure (probability p) (probability q = 1-p. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
In general, (A + B)⁵ = A⁵ + 5A⁴ᵇ + 10A²ᵇ*³ + 10A³ᵇ*² + 5AB⁴ + B⁵
So,
(3–2x)⁵= 3⁵ + 5*3⁴*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5.
Multiplying that by (1 + ax) gives:
3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5 + ax(3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5).
In bold, we find the terms of x^2, so the coefficient of x^2 is 10*3^3*(-2)^2+a*5*3^4*(-2) = 360 - 810a
We know that this must equal 1440, so 360–810a = 1440.
Therefore a= -4/3.
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2. Andrés has 165 baseball cards. He wants to share them equally with his 4 friends.
How many cards will each of his friends get?
Answer:
41
Step-by-step explanation:
NOTE:
The answer can't be a decimal number, because you can't split up cards into quarters like chocolate or bars.
METHOD 1:
Use long division to solve; 4 fits 4 times into 16, and 5 fits 4 times into 1; thus you get 41.
METHOD 2:
You could use it as a fraction, in which you will get 165/4, which as you simplify, is 41 1/4. Since there is no decimal, 1/4 must be removed.
Add 1.5 x 107 to 2.7 x 10.
What is the solution to the system of equations below?
5/2x = y
2x+4/5y=8
A: No solution
B:16/9, 40/9
C: (3, 15/2)
D:(2,5)
Answer:
C
Step-by-step explanation:
[tex]\frac{5}{2}[/tex] x = y → (1)
2x + [tex]\frac{4}{5}[/tex] y = 8 → (2)
substitute y = [tex]\frac{5}{2}[/tex] x into (2)
2x + [tex]\frac{4}{5}[/tex] ([tex]\frac{5}{2}[/tex] ) = 8
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into (1)
y = [tex]\frac{5}{2}[/tex] × 3 = [tex]\frac{15}{2}[/tex]
solution is (3, [tex]\frac{15}{2}[/tex] )
what is the answer to this problem? Evaluate |-7| + 4
Answer:
11 (PLEASE GIVE BRAINLIYEST)
Step-by-step explanation:
absolute value is distance from zero so |-7|=7
and 7+4 is 11
Solve for x in the triangle. Round your answer to the nearest tenth.
The required value of the x in the given right angle triangle is 7.87 unit.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any other angle is a right angle.
In the given triangle,
The given side is 12 unit,
And the angle is 41°.
For any triangle having sides a, b and c and corresponding angles are ∠ A, ∠ B, and ∠ C.
sine formula can be given as,
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]
Since, in the given right angle triangle, one angle is 41° and other angle is 90°.
And their corresponding sides are x unit and 12 unit.
Therefore, sine formula can be applied here,
[tex]\frac{x}{sin41} = \frac{12}{sin90}[/tex]
[tex]\frac{x}{0.656} = \frac{12}{1}[/tex]
x = 7.87
The required value of x is 7.87 unit.
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Select the correct answer. Which of the following is a solution to 4cos2x − 1 = 0? A. 60° B. 150° C. 210° D. 330°
Answer:
60°A is correct
Given:
Divide by 4
Taking square root both sides
Hence, x=60° is correct
The amount of caffeine varies greatly from product to product. Click [here] to examine a table comparing the caffeine content of a variety of drinks. Use the data from the table to answer the questions. Lin made a mixture consisting of 24 ounces of instant tea and 12 ounces of green tea. Approximately how many milligrams of caffeine per ounce were in this final mixture? 0. 02 03. 13 25 45.
The caffeine per ounce in the final mixture of green and instant tea is 40.08 mg.
Based on the data we know quantity of caffeine in an ounce of instant tea is 1368 mg and in green tea is 480.96 mg. So, calculating amount of caffeine in instant and green tea.
Amount of caffeine in instant tea = 24 × 57
Amount of caffeine in instant tea = 1368 mg
Amount of caffeine in green tea = 12 × 6.25
Amount of caffeine in green tea = 75 mg
Total caffeine in the mixture = 1368 + 75
Total caffeine in the mixture = 1443 mg
Total amount of mixture = 12 + 24
Total amount of mixture = 36
Amount of caffeine per ounce in the mixture = 1443/36
Amount of caffeine per ounce in the mixture = 40.08 mg
Hence, the caffeine in mixture is 40.08 mg.
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In the diagram below, quadrilateral STUV is inscribed in circle W. Find the
measure of U.
76⁰
3
W.
77°
The measure of U using the cyclic quadrilateral theorem is 104°.
Cyclic Quadrilateral theoremCyclic quadrilateral theorem states that the sum of the opposite angles of a cyclic quadrilateral is supplementary.
To calcculate the measure of U, we use the cyclic quadrilateral theorem.
From the diagram,
∠S+∠U = 180 (cyclic quadrilateral theorem)................... Equation 1Given:
∠S = 76°Substitute these values into equation 1 and solve for ∠U
∠U+76 = 180∠U = 180-76∠U = 104°Hence, the measure of U is 104°.
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Question 5
Given the values in table, write the equation for the line in slope-intercept form.
X
5
-5
-25
y
-4
-6
3
-10
Answer:
y = 1/5x -5
Step-by-step explanation:
Slope intercept form is y=mx + b where m is the slope and bb is the intercept. Let's find the slope first. This is rise over run, so we take the difference of two points' y-coordinates and divide it by the x-coordinates' difference.
This gives us [tex](-4--6)/(5--5)[/tex], or [tex]2/10[/tex], which simplifies to [tex]1/5[/tex]. This is our slope. Now we have y = 1/5x + b. We now plug in a point to this equation to get b. Plugging in (-25, -10) gives us [tex]-10 = 1/5*-25 + b[/tex], or [tex]-10 = -5 + b[/tex]. From this we get that b = -5. So, our equation is y = 1/5x -5
Feel free to contact me with any questions. I hope this helps!
Use the figure at the right to identify the angle pair relationship.
Angles ∠1 and ∠7 are alternate interior angles and angle ∠4 and ∠8 are adjacent angles.
What are lines and angles?Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and equivalent angles.
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
When a transversal connects two coplanar lines, alternate interior angles are generated. They are on the inside of the parallel lines, but on the outside of the transversal.
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The students in Franklin's class got to choose whether to visit the zoo or the aquarium. 9 students went to the zoo and 16 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the total number of students?
Write your answer as a fraction. Use a forward slash ( / ) to separate the numerator and denomonator
Answer:
9/25
Step-by-step explanation:
total students = 9 + 16 = 25
ratio = 9/25
A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner is divided into two equal sections labeled A and B. Nigel will spin each spinner one time.
How many of the possible outcomes have a number less than 3 or an A?
A.) 9
B.) 5
C.) 7
D.) 2
Answer:
Step-by-step explanation
Man its hard...
pls answer this question
Answer:
Step-by-step explanation:
The answer is C
We have to think about what size 0 would look like, if we observe the change between each figures we can find out the figure grows 4 every time, so we know it's always 4 each time. If we take figure 1 and remove all it's 4 green block it will be just left with 1 yellow block, which is figure 0, we have to add 1 every time we increase the size by 1.
What is the slope of the line through the points x1 y1 and x2 y2?
The slope of a line through the two points is (y2-y1) / (x2 - x1).
The slope of a line:
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
Here we have to find the slope of the line.
Data given:
Point one has the coordinate = (x1, y1)
Point two has the coordinate = (x2, y2)
So the slope of the line(m) =( y2 - y1) / (x2 - x1)
Therefore the slope of the line is (y2- y1) / ) (x2-x1)
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the statement says that you’ve triggered the penalty apr so that it has now increased to 28.99%. what action triggered this?
If you failed to pay the minimum payment by the due date and are now being charged the penalty APR of 28.99%, your monthly interest charge on a balance of $1800 would be approximately $518.82. This is calculated as follows:
$1800 * (28.99% / 12 months) = $518.82However, it is important to note that this calculation is an estimate and the actual amount of interest you would owe in one month could be different, depending on factors such as the number of days in the billing period and the daily interest rate. It is also worth noting that you were charged $6.31 in interest for purchases, which is separate from the interest charged on your unpaid balance.
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a certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. four of the 6 sectors are shaded, and the remaining sectors are not shaded.
The probability that one spin of the spinner will land in a shaded sector is 2/3.
What is meant by probability?The likelihood that something will happen is the straightforward definition of probability. When we are unsure of how an event will turn out, we might talk about the probabilities of various outcomes or how likely they are. The study of events subject to probability is referred to as statistics.
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
When the spinner is released, there is a low likelihood that the part will rest on four.
Information: A particular spinner has equal-sized sectors, and it is equally likely to land in any of them. The remaining sectors are not coloured, and four of the sectors are shaded.
Four of the sectors are shaded, while the remaining sectors are not, according to the enigma.
The spinner has two unshaded areas and four shaded areas.
P(E)=4/6
P(E)=2/3
As a result, there is a simple 2/3 chance that the spinner will rest on four when it is spin.
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The complete question is:
"A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded. What is the probability that one spin of the spinner will land in a shaded sector?"
What is 1/6 as a number?
Answer: 1/6 as a number is 0.1666, with the sixes repeating infinitely, which makes it a rational number. 1/6 = 0.1666 repeating.
Step-by-step explanation: math
Please help me pretty please man
Answer:
b?
Step-by-step explanation:
i think b is right??/
Write the equation of the following lines in slope-intercept form
Answer:
Green Graph: y = x - 6
Red Graph: y = -3/2 + 7
Step-by-step explanation:
Slope intercept form is represented by the formula:
y = mx + b
m is your slope
b is the y intercept
Another thing to note is that, when m is negative, the graph will point to the left, while when m is positive in will point in the right
For the green graph, the line intercepts at -6, so that will be your b value.
the slope is positive 1 because if your count up from -6 and count across to point (1,-5) you get 1/1
Put these pieces of information in your formula and you get
y = x - 6
You can use the same process to find the equation of the red line. However, the slope will be negative since the graph is pointing to the left side of the coordinate plane.
Answer:
Graph 1: y = x - 6
Graph 2: y = -3/2 + 7
The length of a rectangle is 4 meters less than twice its width. The area of the rectangle
is 70 square meters. Find the dimensions of the rectangle. (Area = L·W)
Answer:
The dimensions of the rectangle are 10 meters (L) and 7 meters (W).
Step-by-step explanation:
please give brainliest
What are the three forms of split?
The three forms of split are as follow: splitting , split and splits.
Explanation :
Split is an irregular form of verb.This means 'd' or 'ed' is not added at its end.Irregular verbs are the verbs which does follow the general or regular form of grammar or the normal pattern of change in its form. For example : Eat is ate and eaten not eatted.Considering the first , second , third verb form of split it is same for all.Splitted sounds and is considered wrong .It does align with normal standard of words.Example: Present : I split the bill. Past : I split the billFuture : i shall split the bill.Therefore, the three forms of the split are splitting , split and splits.
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Write an equation in point-slope form, slope-intercept form, and standard form for the following lines:
A. [tex]m = -6; (-9,9)[/tex]
B. [tex](-8,-6); (4,-15)[/tex]
Answer:
Point-slope form:
A. y - 9 = -6(x - 9)
B. y + 6 = -3/2(x + 8)
Slope-intercept form:
A. y = -6x + 63
B. y = -3/2x - 27/2
Standard form:
A. -6x + y - 63 = 0
B. -3/2x - y + 27/2 = 0
Could a scatter graph be used to represent the
data for each of the following? (Yes or No)
a) The heights of different buildings
b) People's favourite sports and their ages
c) The prices of houses and the number of
rooms they have
yes Answer:
Step-by-step explanation: yes
How fast is 150 km in 7200 seconds?
The speed or fastness based on the data of distance and time is 0.02 kilometres per second.
The intensity of fastness is measured by the speed. Concerning this, using the formula of speed to find the how fast the mentioned data indicates.The formula to calculate the speed is -
Speed = distance covered ÷ total time
The distance covered is 150 kilometres and time taken in 7200 seconds. So, the answer will state the speed in kilometres per second. Keep the values in formula to find the speed.
Speed = 150/7200
Performing division on Right Hand Side of the equation to find the speed
Speed = 0.02 kilometres per second.
The mentioned value indicates the object covers 0.02 kilometres in one second.
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Use Standard Form.
Ax + By = C
Answer:
(3,5)
Step-by-step explanation:
5x+3y=15
5(0)+3y=15
3y=15
divide both sides by 3 and you get y=5
5x+3(0)=15
5x=15
divide both sides by 5 and get x= 3
So then the y-int is 5 and the x-int is 3.
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
Help needed was not thought this
Answer:
Yes what is the question
Answer:
what is the question
Step-by-step explanation:
Consider the following table. Is the relationship proportional? Explain your answer.
y
-27
12
57
147
-2
1
4
10
Answer:
The relationship shown in the table is not proportional. A proportional relationship is one in which the ratio of two quantities is always constant. In the table, we can see that the ratio of the values in the y column to the corresponding values in the x column is not constant. For example, the first two values in the y column are -27 and 12, which have a ratio of -27/1 and 12/2, respectively. These ratios are not equal, which indicates that the relationship is not proportional.
Furthermore, if the relationship were proportional, we would expect the values in the y column to increase at a consistent rate as the values in the x column increase. However, this is not the case in the table. For example, the first two values in the x column are 1 and 2, and the corresponding values in the y column are -27 and 12. The difference between these values is -27 - 12 = -39, which is a large negative value. However, the difference between the next two values in the y column is 57 - 147 = -90, which is a much larger negative value. This indicates that the relationship is not proportional, because the differences between the y values do not increase at a consistent rate as the x values increase.
Step-by-step explanation:
2x - 3y = -1
y =x -1
Substitution
Answer:
x = 4 ; y = 3
Step-by-step explanation:
2x - 3(x-1) = -1
2x - 3x + 3 = -1
- x = -1 - 3
- x = -4
x = 4
y = 4-1
y = 3
The following table shows the breakdown of opinions for both faculty and students in a recent survey about the new restructuring of the campus to include an Honors College. Find the probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or against. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Survey Results on Restructuring Campus to Include an Honors College
Category Favor Oppose Neutral Total
Faculty 6 15 15 36
Students 41 41 58 140
Total 47 56 73 176
The probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or against is given as follows:
31/88.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes in this problem is given as follows:
176 people.
The desired outcomes are given as follows:
Student opposed to the change: 41.Faculty member who is either for or against: 6 + 15 = 21.(these outcomes are both calculated from the data given by the table).
Hence the probability is calculated as follows:
p = (41 + 21)/176 = 62/176 = 31/88.
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